As a mechanical design engineer specializing in high-precision five-axis machine tools, I have devoted considerable effort to the development of dual swivel heads, also known as fork-type milling heads or five-axis heads. These units enable continuous rotation of the spindle as well as coordinated A-axis and C-axis movements, which together with the linear X, Y, Z axes form a five-coordinate machining system. In this article, I will share my experience and technical insights into the worm gear backlash elimination structure used in mechanical dual swivel heads, a critical component that ensures high positioning accuracy and sustained performance under heavy cutting conditions.
The dual swivel head I have been working on is designed for large-torque, heavy-duty applications such as shipbuilding, mining, and locomotive manufacturing. The spindle drive is implemented through a gear train, while the A and C axes are driven by worm gear pairs. This traditional architecture provides excellent torque capacity, but it inherently suffers from friction and wear over time, leading to increased backlash between the worm and the worm wheel. For a five-axis machine with a rotary resolution of 0.001°, even minute clearance can severely degrade the repeatability and contouring accuracy. Therefore, a reliable backlash elimination mechanism for the worm gear is essential.
The mechanical dual swivel head is compact but complex. It houses three independent drive systems: the main spindle motor, the A-axis swing motor, and the C-axis rotary motor. All three must be integrated within a limited space, which makes design, manufacturing, and assembly extremely challenging. The worm gear used for the C-axis rotary motion is especially demanding. Below, I summarize the key parameters of the mechanical dual swivel head I have been involved with:
| Parameter | Value |
|---|---|
| Spindle power (S1/S6) | 28 / 43 kW |
| Maximum spindle speed | 5,600 r/min |
| Maximum spindle torque (S1/S6) | 638 / 971 N·m |
| A/C-axis rotary speed | 25° / s |
| A/C-axis rotary resolution | 0.001° |
| A/C-axis drive torque | 7,000 N·m |
| A/C-axis clamping torque | 20,000 N·m |
| Tool holder interface | BT50 / JT50 |
| Tool clamping method | Disc spring (hydraulic release) |
| Distance from swing axis to spindle nose | 270 mm |
| A-axis swing range | ±100° |
| C-axis rotary range | ±n×360° (unlimited) |
From these numbers, it is evident that the required rotary resolution of 0.001° demands an extremely precise worm gear pair. Any significant backlash would lead to poor repeatability and unacceptable contour errors in five-axis machining. Conventional worm gear drives rely on fixed center distances and are prone to increasing clearance after a period of operation due to wear. To solve this, I adopted a split worm design with an adjustable axial clearance compensation mechanism, which is the core topic of this article.
Worm Gear Backlash Problem and Design Principle
In a standard worm gear transmission, the sliding contact between the worm threads and the worm wheel teeth generates friction and wear. Over time, the tooth flank thickness reduces, widening the backlash. For a high-precision dual swivel head, backlash must be minimized and maintained within a few arc-seconds throughout the service life. Instead of using complicated spring-loaded or eccentric mechanisms, I designed a split worm structure that allows easy axial adjustment to compensate for wear.
The split worm consists of two coaxial parts: a sleeve worm and a shaft worm. The shaft worm has an inserted cylindrical portion that fits into the bore of the sleeve worm. Both parts are fixed together via a key or spline connection, so they rotate as one unit. However, the two worms have separate helical threads that together form a continuous worm thread when properly aligned. The sleeve worm is mounted on one side with a bearing, and the shaft worm is supported by another bearing on the opposite side. Between the bearing housing and the worm body, a shim (adjusting pad) is placed. By changing the thickness of this shim, the axial position of the entire worm assembly relative to the worm wheel can be shifted, thereby adjusting the mesh clearance.
The principle relies on the fact that the worm thread is essentially a helical ramp. Axial movement of the worm relative to the worm wheel changes the radial distance between the thread flanks and the wheel teeth. The relationship between axial displacement \(\Delta x\) and the resulting change in backlash (radial clearance) \(\Delta c\) is given by the lead angle \(\lambda\) of the worm:
$$\Delta c = \Delta x \cdot \tan \lambda$$
where \(\tan \lambda = \frac{p_z}{\pi d_1}\), \(p_z\) is the axial pitch (lead) of the worm, and \(d_1\) is the pitch diameter of the worm. This simple formula allows us to determine the required shim thickness adjustment to restore the optimal meshing condition.
In my design, the worm gear pair for the C-axis has the following geometric parameters:
| Parameter | Symbol | Value | Unit |
|---|---|---|---|
| Module (axial) | \(m\) | 6 | mm |
| Number of worm starts | \(z_1\) | 1 | – |
| Number of wheel teeth | \(z_2\) | 60 | – |
| Worm pitch diameter | \(d_1\) | 72 | mm |
| Worm wheel pitch diameter | \(d_2\) | 360 | mm |
| Lead angle | \(\lambda\) | 4.76° | deg |
| Axial pitch (lead) | \(p_z\) | 18.85 | mm |
| Center distance | \(a\) | 216 | mm |
| Pressure angle | \(\alpha\) | 20° | deg |
From the lead angle \(\lambda = 4.76^\circ\), for every 1 mm of axial shim reduction, the radial backlash reduces by approximately \( \tan(4.76^\circ) \approx 0.0833\) mm. This allows very fine and predictable compensation. In practice, we typically set the initial shim thickness such that a slight preload is applied to eliminate any clearance while still allowing free rotation. After some operating hours, when backlash begins to appear, we replace the shim with a slightly thinner one to move the worm axially towards the worm wheel, restoring the zero-backlash condition.
The axial adjustment also influences the contact pattern. A proper shim thickness ensures that the line of contact remains centered on the worm wheel teeth. Too much axial shift could cause edge loading and accelerate wear. Therefore, I also developed a calculation for the optimal shim range based on the permissible axial movement \(\Delta x_{max}\):
$$\Delta x_{max} = \frac{b_2}{2 \tan \lambda}$$
where \(b_2\) is the face width of the worm wheel. For our design, \(b_2 = 48\) mm, giving \(\Delta x_{max} \approx 24\) mm. This is far more than needed; typically, adjustments of 0.1–0.5 mm are sufficient.
Detailed Split Worm Assembly Design
As shown conceptually, the split worm comprises two parts: the sleeve worm (outer part with internal bore) and the shaft worm (inner part with external thread and a shaft extension). The sleeve worm has its own set of helical threads, while the shaft worm also has threads that are cut to match the same helix. When assembled, the two thread sets align precisely, forming a continuous worm thread. The connection between the two parts is via a precision ground key and a clamping arrangement. The assembly is mounted on two tapered roller bearings that support axial and radial loads. On one side, the bearing is retained by a nut, and a shim ring is placed between the bearing outer race and the housing shoulder. Adjusting the shim thickness changes the axial position of the entire worm.
To ensure that the two halves of the worm gear remain synchronized, the key is designed to have zero clearance, and the clamping force is applied via a lock nut and a locking mechanism. In production, we pre-assemble the split worm and measure the overall axial runout of the combined thread. Then we grind the shim to achieve the desired zero-backlash mesh with the worm wheel. The tolerance for the axial adjustment is typically ±0.01 mm.
Torque and Efficiency Considerations
The worm gear pair must transmit a drive torque of 7,000 N·m continuously, with a clamping torque of 20,000 N·m. The efficiency of a worm gear is given by:
$$\eta = \frac{\tan \lambda}{\tan(\lambda + \phi)}$$
where \(\phi = \arctan \mu\) is the friction angle, and \(\mu\) is the coefficient of friction. For bronze-on-steel with good lubrication, \(\mu \approx 0.05\) to 0.10. Taking \(\mu = 0.08\), we have \(\phi \approx 4.57^\circ\). With \(\lambda = 4.76^\circ\), the efficiency is:
$$\eta = \frac{\tan 4.76^\circ}{\tan(4.76^\circ + 4.57^\circ)} \approx \frac{0.0833}{0.1635} \approx 0.51$$
This moderate efficiency (about 51%) is typical for single-start worm gears. The self-locking condition requires \(\lambda < \phi\), but here \(\lambda > \phi\), so the drive is not self-locking. In the dual swivel head, we rely on the brake system to hold the position when the motor is off.
The tangential force on the worm wheel \(F_{t2}\) is related to the output torque \(T_2 = 7000\) N·m:
$$F_{t2} = \frac{2 T_2}{d_2} = \frac{2 \times 7000}{0.36} \approx 38,889 \, \text{N}$$
The axial force on the worm \(F_{a1}\) equals \(F_{t2}\) times the lead angle factor:
$$F_{a1} = F_{t2} \cdot \tan \lambda \approx 38,889 \times 0.0833 \approx 3,239 \, \text{N}$$
This axial force is supported by the tapered roller bearings. The shim adjustment must be performed with the drive unloaded, as any axial load would cause the worm to bind if the adjustment is too tight.
Comparison with Other Backlash Elimination Methods
There are several common approaches to eliminate backlash in worm gear drives. I have compared them in the table below:
| Method | Principle | Advantages | Disadvantages |
|---|---|---|---|
| Split worm (axial adjustment) | Two-part worm moved axially via shim | Simple, reliable, easy to adjust in field, no extra parts | Requires disassembly to change shim; not automatic |
| Spring-loaded floating worm | Worm pressed against wheel by spring force | Automatic compensation; constant preload | Reduces torque capacity; wear may cause spring fatigue |
| Eccentric bearing housing | Rotating housing changes center distance | Continuous adjustment possible without disassembly | Complex machining; requires precise indexing; limited range |
| Dual worm (back-to-back) | Two worms driving same wheel with spring preload | Very high stiffness; zero backlash even under reversing load | Bulky; high cost; difficult to align |
For our heavy-duty dual swivel head, the split worm with shim adjustment provides the best balance between simplicity, cost, and reliability. The machine tool is designed for long production runs, and scheduled maintenance can easily include shim replacement. We also provide a calculation chart that operators can use to determine the exact shim thickness based on measured backlash after a certain number of operating hours.
Backlash Measurement and Adjustment Procedure
During assembly and maintenance, we measure the backlash using a dial indicator placed at the outer diameter of the worm wheel. With the worm stationary, we rock the worm wheel back and forth and record the angular displacement. The backlash angle \(\theta_b\) (in degrees) is related to the linear clearance at the pitch circle:
$$\theta_b = \frac{360 \times c}{\pi d_2}$$
where \(c\) is the radial backlash. Our target after adjustment is \(c \leq 0.02\) mm, which corresponds to \(\theta_b \leq 0.0064^\circ\) (about 23 arc-seconds). The actual resolution of 0.001° requires even tighter control, but the worm gear backlash contributes only part of the total error; the rest comes from the servo system and bearings. We typically aim for backlash below 10 arc-seconds at the worm wheel output.
To adjust, we first remove the bearing cap on the shaft worm side, take out the existing shim, and measure its thickness \(t_{old}\). Then we measure the current backlash \(\theta_b\). The required reduction in radial clearance \(\Delta c\) is:
$$\Delta c = c_{current} – c_{target}$$
Then the shim thickness change \(\Delta t\) is:
$$\Delta t = \frac{\Delta c}{\tan \lambda}$$
If \(c_{current} > c_{target}\), we need to decrease the shim thickness (move worm axially toward the wheel). Therefore, the new shim thickness \(t_{new} = t_{old} – \Delta t\). We then grind or select a shim with the new thickness, reassemble, and verify the backlash. Typically, one adjustment cycle reduces the backlash by the desired amount and extends the life of the worm gear pair by thousands of hours.
Material Selection and Lubrication
The worm in our design is made of case-hardened alloy steel (e.g., 20CrMnTi) with surface hardness HRC 58–62, ground to a high surface finish. The worm wheel is made of high-quality phosphor bronze (CuSn12Ni2) to ensure good wear resistance and low friction. The lubricant is a high-viscosity EP gear oil (ISO VG 460) with extreme pressure additives. The housing is sealed to prevent contamination. The split design does not affect the lubrication channel; oil is supplied through a nozzle directly onto the mesh zone.
In the field, we have observed that after 2,000 hours of operation under cutting loads up to 70% of maximum torque, the backlash increases by about 0.01-0.02 mm. A single shim adjustment restores the original precision. After several adjustments, the worm wheel may need replacement, but the worm can be reused if it shows minimal wear. The split worm construction also allows the sleeve worm to be replaced independently if only one thread set is damaged.
Conclusion
The worm gear backlash elimination structure based on the split worm with adjustable shims has proven to be a robust and cost-effective solution for mechanical dual swivel heads used in heavy-duty five-axis machining. My design ensures that the A and C axes maintain high positional accuracy over extended periods, enabling the machine to produce complex parts such as impellers, propellers, and large structural components with tight tolerances. The simple axial adjustment mechanism can be implemented without major modifications to the existing housing, and the required maintenance is straightforward for trained technicians.
The worm gear remains the heart of the rotary drive in traditional heavy-duty swivel heads. Even as electric spindle technology advances, mechanical drives still dominate applications demanding high torque and rigidity. By continuously refining the worm gear design—including the backlash elimination mechanism—we are able to match or exceed the performance of imported units. The table below summarizes the final design parameters of the worm gear pair after optimization:
| Item | Value |
|---|---|
| Worm material | 20CrMnTi, HRC 58-62 |
| Worm wheel material | CuSn12Ni2 bronze |
| Number of starts | 1 |
| Axial module | 6 mm |
| Worm pitch diameter | 72 mm |
| Worm wheel pitch diameter | 360 mm |
| Lead angle | 4.76° |
| Center distance | 216 mm |
| Face width of worm wheel | 48 mm |
| Maximum shim adjustment range | ±2 mm |
| Target backlash (after adjustment) | ≤ 0.02 mm (radial) |
| Efficiency (theoretical) | ~51% |
The successful implementation of this worm gear backlash elimination structure has contributed significantly to the domestic development of high-end dual swivel heads, reducing dependence on foreign suppliers and enabling local manufacturing of complex aerospace and energy components. In my ongoing work, I continue to explore ways to integrate condition monitoring and automatic adjustment, but the manual shim method remains the most reliable for the heavy-duty environment.